In a wide variety of modern applications, it is desirable to observe the three dimensional coherence of a volume or object of interest. In the case of imaging real three dimensional ( "3D") solids, ordinarily it is only possible to view discrete planar cross sections of the 3D volume and its contents. It is not possible typically to view 3D volumes such that internal and object surfaces, boundaries, interfaces, and spatial relationships within the volume can be separated and indentified visually.
In medical imaging, for example, it is highly desirable to be able to visualize anatomical structures by three dimensional representations on computer graphic displays. The ability to produce accurate, volmetric, anatomical models from computerized tomographic (CT) scans is extremely valuable as a surgical aid, (such as for displaying structures to plan surgical intervention, or to represent details of the anatomical structure without the need for exploratory surgery). Thus, the 3D shape, size and relative position of pathologic structures provides important data for surgical planning, diagnosis and treatment.
Computer simulation of real 3D volumes depends on the ability to reconstruct 3D structures from planar section data, such as CT scans. These and other scans provide data from which a 3D density image volume consisting volume elements (voxels) is available as input data for image processing. Unfortunately, such input image volumes are typically of low resolution as compared to the level of detail desired to represent accurately the sampled volume.
For example, in CT scan image volumes, voxels represent x-ray attenuation or other image volume data throughout the volume, including across surface boundaries. Although a voxel is assigned only a single "homogenous" value, in fact there exists a boundary and discrete materials on either side of the boundary within the object under consideration. Thus, a voxel along an edge is a sample extending over both sides of the edge. Further, if a material (such as a bone) is less that one voxel wide, the voxel that provides boundary information about that bone is very low resolution. Thus, the boundary shape within a voxel is not readily determined.
Various approaches have been used in an effort to approximate surface boundaries within volumes. One well known method is "thresholding". In thresholding, voxels that cross a boundary are classified as being composed of one or the other material type on either side of the boundary . The projected visible boundary thus becomes the binary classified voxel border.
The larger the voxels , the greater the error that is introduced by thresholding. Further, for coarse images or images with high density and closely spaced surface boundaries, thresholding provides an even further degraded result, such that the resultant images become less and less accurate. Subsequent approximation techniques are sometimes used in an attempt to render a more accurate approximation from the thresholding result. However, attempts to approximate the unknown surface gives rise to a grossly inaccurate result since these approximations rely on the initial binary classification of the voxels.
It is also highly desirable to be able to view all the data within the volume simultaneously from selected stationary or rotating views; that is, to view into the center of a volume, and to detect objects and hidden surfaces within the volume (and therefore internal boundaries and surfaces). To do so, it is necessary to be able to see partially through interfering objects when desired (e.g., for bone surrounded by muscle, to be able to observe the bone as well as the muscle surrounding the bone). Prior art techniques, for rendering volume elements which forces a binary decision to be made as to whether a pixel is made of a given material or not. A binary classification introduces aliasing (or sampling) errors as the continuous image function is not preserved. The error introduced by binary classification is introduced upon any attempt to reconstruct the original image volume from the classified volume. Because the reconstructed image can only have as many intensity levels as there are materials, material interfaces will be jagged and the intensities will not represent the original image function.